Earlier quoted context omitted.
Do you definitely want to transfer kinetic energy more than momentum? I reckon a lighter hammer swung faster is more likely to end up with a bent nail. Also, exponential would be 2^v. v^2 is quadratic. (And you need to sub in the F=ma part as well to demonstrate your point, so your gain from the lighter hammer should be less than quadratic. Exercise left to the reader.)
> Do you definitely want to transfer kinetic energy more than momentum? Seems that way; if you're using a hammer, the goal is for all parts of the system to come to a stop. You're trying to deform the material you're hammering the nail into; isn't that measured in energy transfer?
Intuitively, I feel like weighty hits tend to drive the nail into the wood, whereas fast hits just bash the nail about. That might be more about accuracy though?
(Also my anecdote confirmed by someone with practical experience, see other comment.)